1. Field of the Invention
This invention generally relates to a frequency synthesis system and, more particularly, to a system and method to support either rational or irrational number frequency division.
2. Description of the Related Art
FIG. 1 is a schematic block diagram depicting an accumulator circuit capable of performing a division operation prior art). As noted in “A Pipelined Noise Shaping Coder for Fractional-N Frequency Synthesis”, by Kozak et al., IEEE Trans. on Instrumentation and Measurement, Vol. 50, No. 5, October 2001, the depicted 4th order device can be used to determine a division ratio using an integer sequence.
The carry outs from the 4 accumulators are cascaded to accumulate the fractional number. The carry outs are combined to reduce quantization noise by adding their contributions are follows:contribution 1=c1[n]; contribution 2=c2[n]−c2[n−1];contribution 3=c3[n]−2c3[n−1]+c3[n−2];contribution 4=c4[n]−3c4[n−1]+3c4[n−2]−c4[n−3];
where n is equal to a current value, and (n−1) is the previous value.
FIG. 2 shows the contributions made by the accumulator depicted in FIG. 1 with respect to order (prior art). A fractional number is a number that expresses a ratio of a numerator divided by a denominator. Some fractional numbers are rational—meaning that the numerator and denominator are both integers. With an irrational number, either the numerator or denominator is not an integer (e.g., π). Some rational numbers cannot be resolved (e.g., 10/3), while other rational numbers may only be resolved using a large number of decimal (bit) places. In these cases, or if the fractional number is irrational, a long-term mean of the integer sequence must be used as an approximation.
It would be advantageous if a division circuit existed where the quotient could be obtained by using a dividend and divisor ratio that is a rational number. It would advantageous if the above-mentioned division circuit could also operate with a dividend and divisor expressed as an irrational number.